Linear independence and orthogonality of vectors
okay, so this is really two questions, the first is kind of simple:
if a+b=0, a+c=0 and c=b can it be shown that a+b+c=0? (without the use of determinants)
The second is: what is an example of a set of vectors that are linearly independent but not orthogonal? (graphical interpretation would be appreciated)
Re: Linear independence and orthogonality of vectors
Knowing , and (which follows from the first two equations) it does not always follow that Try playing around with some specific values for to see why.
For the second question, thinking about might be the easiest place to look. Geometrically, two vectors are linearly indepdent in if they don't lie on the same line through the origin. It may be simplest to take one of the vectors to be To find a second vector that is linearly independent from and is not orthogonal to it means we should pick a vector that does not sit on the -axis and is not perpendicular to the -axis.
Does this get things going in the right direction? Let me know if anything is unclear. Good luck!